Steps to get the special ending with info given after you beat the game once.
Guide to Get the Special Ending (Spoiler Alert)
At the end of the game, you get this message for a password.
Start a new game, and at the beginning go into the house.
There is a guy in a red hoodie and a computer in there.
Enter the password you saw on the computer.
He starts freaking out and runs off to change his hoodie to a tinfoil one.
After he runs off, a chest appears with a torn paper. It seems to give clues. There are four alien craft to fight through out the game in order to get the special ending.
First one is located behind the teapot on top of a tall building in Roke. Walk up the alley in the middle and turn right.
Second one you can get right after you buy the foglight. Go up to the Northwest, climb up and you'll find it on the hill.
Third one is located where the orphanage gate used to be after you get back on the third day.
Last one is located in the area you get gas for the car near where you find the store-room keys. You will not be able to get this if you do the "memories" ending. Only after you Climb the tower and the bomb goes off.
You'll get "unidentified objects" every time you beat one. 1x for the first 2x for the second and so forth. You can't use them, but I imagine they're necessary to trigger the final ending.
After you get through Vurrus' mansion (with the mirrors), and you have collected everything you are supposed to, you are greeted with the four flying saucers and you end up fighting a big mother ship one in a final battle. Be sure to save and level up a bit as it's a tough one.
This unlocks the "Beyond the Garden..." achievement as well.